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Logical reasoning lesson 22: Venn diagrams · Set 41 · 40 questions
TalentJR

How to think it through (Middle first): Put “both” in the overlap. Only A = A − both; only B = B − both; at least one = A + B − both. Neither = total − at least one; exactly one = only A + only B.

NameDateTime takenScore ___ / 40
  1. 1.In a group of 31 children, 23 play cricket, 17 play football and 12 play both. How many play exactly one of the two?
  2. 2.In a group of 32 grown-ups, 21 drink tea, 15 drink coffee and 6 drink both. How many drink exactly one of the two?
  3. 3.In a group of 24 grown-ups, 14 drink tea, 11 drink coffee and 5 drink both. How many drink only tea?
  4. 4.In a group of 26 children, 13 like mangoes, 16 like bananas and 9 like both. How many like only mangoes?
  5. 5.In a group of 41 grown-ups, 29 drink tea, 19 drink coffee and 9 drink both. How many drink only coffee?
  6. 6.In a group of 42 children, 16 play chess, 22 play carrom and 2 play both. How many play only chess?
  7. 7.In a group of 43 children, 22 enjoy drawing, 27 enjoy dancing and 12 enjoy both. How many enjoy only drawing?
  8. 8.In a group of 49 grown-ups, 29 drink tea, 19 drink coffee and 10 drink both. How many drink only coffee?
  9. 9.In a group of 40 children, 16 like mangoes, 22 like bananas and 8 like both. How many like neither of the two?
  10. 10.In a group of 53 children, 31 sing Hindi songs, 32 sing English songs and 12 sing both. How many sing at least one of the two?
  11. 11.In a group of 29 children, 16 play chess, 12 play carrom and 9 play both. How many play exactly one of the two?
  12. 12.In a group of 48 children, 16 enjoy drawing, 23 enjoy dancing and 6 enjoy both. How many enjoy exactly one of the two?
  13. 13.In a group of 44 children, 14 sing Hindi songs, 23 sing English songs and 6 sing both. How many sing at least one of the two?
  14. 14.In a group of 51 children, 32 play chess, 25 play carrom and 12 play both. How many play only carrom?
  15. 15.In a group of 28 children, 19 enjoy drawing, 7 enjoy dancing and 3 enjoy both. How many enjoy neither of the two?
  16. 16.In a group of 26 children, 9 play cricket, 15 play football and 5 play both. How many play only cricket?
  17. 17.In a group of 34 children, 24 enjoy drawing, 10 enjoy dancing and 6 enjoy both. How many enjoy at least one of the two?
  18. 18.In a group of 53 children, 20 sing Hindi songs, 24 sing English songs and 5 sing both. How many sing only Hindi songs?
  19. 19.In a group of 54 children, 24 play chess, 30 play carrom and 11 play both. How many play only chess?
  20. 20.In a group of 34 grown-ups, 14 drink tea, 19 drink coffee and 6 drink both. How many drink at least one of the two?
  21. 21.In a group of 33 children, 8 play chess, 25 play carrom and 5 play both. How many play only carrom?
  22. 22.In a group of 43 children, 20 play cricket, 19 play football and 9 play both. How many play only cricket?
  23. 23.In a group of 39 children, 25 play chess, 16 play carrom and 6 play both. How many play only carrom?
  24. 24.In a group of 40 children, 16 sing Hindi songs, 28 sing English songs and 12 sing both. How many sing only English songs?
  25. 25.In a group of 49 children, 16 sing Hindi songs, 26 sing English songs and 8 sing both. How many sing exactly one of the two?
  26. 26.In a group of 33 children, 16 enjoy drawing, 19 enjoy dancing and 7 enjoy both. How many enjoy only dancing?
  27. 27.In a group of 39 children, 13 play chess, 19 play carrom and 4 play both. How many play only chess?
  28. 28.In a group of 40 children, 30 play cricket, 16 play football and 11 play both. How many play only cricket?
  29. 29.In a group of 45 grown-ups, 24 drink tea, 16 drink coffee and 4 drink both. How many drink neither of the two?
  30. 30.In a group of 21 grown-ups, 12 drink tea, 14 drink coffee and 7 drink both. How many drink only coffee?
  31. 31.In a group of 20 children, 10 sing Hindi songs, 12 sing English songs and 6 sing both. How many sing exactly one of the two?
  32. 32.In a group of 24 grown-ups, 9 drink tea, 12 drink coffee and 6 drink both. How many drink at least one of the two?
  33. 33.In a group of 29 children, 23 play cricket, 11 play football and 6 play both. How many play only football?
  34. 34.In a group of 50 grown-ups, 19 drink tea, 27 drink coffee and 11 drink both. How many drink exactly one of the two?
  35. 35.In a group of 43 children, 24 play cricket, 19 play football and 4 play both. How many play only cricket?
  36. 36.In a group of 28 children, 10 like mangoes, 6 like bananas and 3 like both. How many like exactly one of the two?
  37. 37.In a group of 31 children, 19 enjoy drawing, 8 enjoy dancing and 2 enjoy both. How many enjoy only drawing?
  38. 38.In a group of 34 grown-ups, 14 drink tea, 28 drink coffee and 11 drink both. How many drink only coffee?
  39. 39.In a group of 29 children, 17 play cricket, 16 play football and 7 play both. How many play only cricket?
  40. 40.In a group of 42 grown-ups, 20 drink tea, 9 drink coffee and 2 drink both. How many drink only coffee?

Answer key

  1. 16
  2. 24
  3. 9
  4. 4
  5. 10
  6. 14
  7. 10
  8. 9
  9. 10
  10. 51
  11. 10
  12. 27
  13. 31
  14. 13
  15. 5
  16. 4
  17. 28
  18. 15
  19. 13
  20. 27
  21. 20
  22. 11
  23. 10
  24. 16
  25. 26
  26. 12
  27. 9
  28. 19
  29. 9
  30. 7
  31. 10
  32. 15
  33. 5
  34. 24
  35. 20
  36. 10
  37. 17
  38. 17
  39. 10
  40. 7

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